Chapter 8.1, Problem 19PPS

To determine

The value of x, y and z.

Answer to Problem 19PPS

  $\begin{array}{l}y=\frac{325}{6}=54.2\\ x=5\sqrt{13}=18.0\\ z=\frac{85\sqrt{13}}{6}=51.1\end{array}$

Explanation of Solution

Given:

The given figure is:

Calculation:

According to Geometric Mean Altitude Theorem,

  $\begin{array}{l}17=\sqrt{6\left(y-6\right)}\\ {17}^2=6\left(y-6\right)\\ 289=6y-36\\ 6y=325\\ y=\frac{325}{6}=54.2\end{array}$

According to Geometric Mean Leg Theorem,

  $\begin{array}{l}x=\sqrt{6y}\\ x=\sqrt{6\left(\frac{325}{6}\right)}\\ x=\sqrt{325}\\ x=5\sqrt{13}\\ \text{and}\\ z=\sqrt{y\left(y-6\right)}\\ z=\sqrt{\frac{325}{6}\left(\frac{325}{6}-6\right)}\\ z=\sqrt{\frac{93925}{36}}\\ z=\frac{85\sqrt{13}}{6}\end{array}$